man pages section 3: Multimedia Library Functions
Updated: July 2014

## mlib_SignalLPC2LSP_F32 (3MLIB)

### Name

mlib_SignalLPC2LSP_F32 - convert linear prediction coefficients to line spectral pair coefficients

### Synopsis

```cc [ flag... ] file... –lmlib [ library... ]
#include <mlib.h>

mlib_status mlib_SignalLPC2LSP_F32(mlib_f32 *lsp, const mlib_f32 *lpc,
mlib_s32 order);```

### Description

The mlib_SignalLPC2LSP_F32() function converts linear prediction coefficients to line spectral pair coefficients.

The line spectral pair (LPS) coefficients are defined as the roots of the following two polynomials:

```	               -(M+1)     -1
P(z) = A(z) + z      * A(z  )

-(M+1)     -1
Q(z) = A(z) - z      * A(z  )
```

where A(z) is the inverse filter

```	           M          -i
A(z) = 1- SUM a(i) * z
i=1
```

Note that since P(z) is symmetric and Q(z) is antisymmetric all roots of these polynomials are on the unit circle and they alternate each other. P(z) has a root at z = -1 (w = PI) and Q(z) has a root at z = 1 (w = 0).

The line spectral frequency (LPF) are the angular frequency of the line spectral pair (LPS) coefficients.

```	q = cos(w)
```

where q is the LPS and w is the LPF.

See Fundamentals of Speech Recognition by Lawrence Rabiner and Biing-Hwang Juang, Prentice Hall, 1993.

### Parameters

The function takes the following arguments:

lsp

The line spectral pair coefficients.

lpc

The linear prediction coefficients.

order

The order of the linear prediction filter.

### Return Values

The function returns MLIB_SUCCESS if successful. Otherwise it returns MLIB_FAILURE.

### Attributes

See attributes(5) for descriptions of the following attributes:

ATTRIBUTE TYPE
ATTRIBUTE VALUE
Interface Stability
Committed
MT-Level
MT-Safe